Problem: Solve for $x$ and $y$ using elimination. ${3x-6y = -24}$ ${3x-5y = -17}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-3x+6y = 24}$ $3x-5y = -17$ Add the top and bottom equations together. ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {3x-6y = -24}\thinspace$ to find $x$ ${3x - 6}{(7)}{= -24}$ $3x-42 = -24$ $3x-42{+42} = -24{+42}$ $3x = 18$ $\dfrac{3x}{{3}} = \dfrac{18}{{3}}$ ${x = 6}$ You can also plug ${y = 7}$ into $\thinspace {3x-5y = -17}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(7)}{= -17}$ ${x = 6}$